Please read this section of Wikipedia which talks about these topics better than I could
Please read Maths textbooks which explain it better than Joe Blow Your next Door neighbour on Wikipedia. there’s plenty in here
It shows that there is ambiguity in the order of operations
and is wrong about that, as proven by Maths textbooks
especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication
That’s because Multiplication and Division can be done in any order
It addresses everything you’ve mentioned
wrongly, as per Maths textbooks
Multiplication denoted by juxtaposition (also known as implied multiplication)
Nope. Terms/Products is what they are called. “implied multiplication” is a “rule” made up by people who have forgotten the actual rules.
s often given higher precedence than most other operations
Always is, because brackets first. ab=(axb) by definition
1 / 2n is interpreted to mean 1 / (2 · n)
As per the definition that ab=(axb), 1/2n=1/(2xn).
[2][10][14][15]
Did you look at the references, and note that there are no Maths textbooks listed?
the manuscript submission instructions for the Physical Review journals
Which isn’t a Maths textbook
the convention observed in physics textbooks
Also not Maths textbooks
mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik
Actually that is a Computer Science textbook, written for programmers. Knuth is a very famous programmer
More complicated cases are more ambiguous
None of them are ambiguous.
the notation 1 / 2π(a + b) could plausibly mean either 1 / [2π · (a + b)]
It does as per the rules of Maths, but more precisely it actually means 1 / (2πa + 2πb)
or [1 / (2π)] · (a + b).[18]
No, it can’t mean that unless it was written (1 / 2π)(a + b), which it wasn’t
Sometimes interpretation depends on context
Nope, never
more explicit expressions (a / b) / c or a / (b / c) are unambiguous
a/b/c is already unambiguous - left to right. 🙄
Image of two calculators getting different answers
With the exception of Texas Instruments, all the other calculator manufacturers have gone back to doing it correctly, and Sharp have always done it correctly.
6÷2(1+2) is interpreted as 6÷(2×(1+2))
6÷(2x1+2x2) actually, as per The Distributive Law, a(b+c)=(ab+ac)
(6÷2)×(1+2) by a TI-83 Plus calculator (lower)
Yep, Texas Instruments is the only one still doing it wrong
This ambiguity
doesn’t exist, as per Maths textbooks
“8 ÷ 2(2 + 2)”, for which there are two conflicting interpretations:
No there isn’t - you MUST obey The Distributive Law, a(b+c)=(ab+ac)
Mathematics education researcher Hung-Hsi Wu points out that “one never gets a computation of this type in real life”
If you believe the article is incorrect, submit your corrections to Wikipedia
You know they’ve rejected corrections by actual Maths Professors right? Just look for Rick Norwood in the talk section. Everyone who knows Maths knows Wikipedia is wrong, and looks in the right place to begin with - Maths textbooks
Again, if you have a problem with Wikipedia, take it up with Wikipedia
You’ve made the mistake of thinking they care. Again, look for Rick Norwood in the Talk sections, an actual Maths professor (bless him for continually trying to get them to correct the mistakes though)
I did read everything you said and I do know how to do math. I hope you are able to enact the change you want to see in Wikipedia and the article. Good luck.
Please read Maths textbooks which explain it better than Joe Blow Your next Door neighbour on Wikipedia. there’s plenty in here
and is wrong about that, as proven by Maths textbooks
That’s because Multiplication and Division can be done in any order
wrongly, as per Maths textbooks
Nope. Terms/Products is what they are called. “implied multiplication” is a “rule” made up by people who have forgotten the actual rules.
Always is, because brackets first. ab=(axb) by definition
As per the definition that ab=(axb), 1/2n=1/(2xn).
Did you look at the references, and note that there are no Maths textbooks listed?
Which isn’t a Maths textbook
Also not Maths textbooks
Actually that is a Computer Science textbook, written for programmers. Knuth is a very famous programmer
None of them are ambiguous.
It does as per the rules of Maths, but more precisely it actually means 1 / (2πa + 2πb)
No, it can’t mean that unless it was written (1 / 2π)(a + b), which it wasn’t
Nope, never
a/b/c is already unambiguous - left to right. 🙄
With the exception of Texas Instruments, all the other calculator manufacturers have gone back to doing it correctly, and Sharp have always done it correctly.
6÷(2x1+2x2) actually, as per The Distributive Law, a(b+c)=(ab+ac)
Yep, Texas Instruments is the only one still doing it wrong
doesn’t exist, as per Maths textbooks
No there isn’t - you MUST obey The Distributive Law, a(b+c)=(ab+ac)
And he was wrong about that. 🙄
Which notably can be found in Maths textbooks
If you believe the article is incorrect, submit your corrections to Wikipedia instead of telling me.
You know they’ve rejected corrections by actual Maths Professors right? Just look for Rick Norwood in the talk section. Everyone who knows Maths knows Wikipedia is wrong, and looks in the right place to begin with - Maths textbooks
Again, if you have a problem with Wikipedia, take it up with Wikipedia.
You’ve made the mistake of thinking they care. Again, look for Rick Norwood in the Talk sections, an actual Maths professor (bless him for continually trying to get them to correct the mistakes though)
Take it up with them if you have a problem with them.
I see you’re not even reading what I said. No wonder you don’t know how to do Maths…
I did read everything you said and I do know how to do math. I hope you are able to enact the change you want to see in Wikipedia and the article. Good luck.
Clearly you didn’t, given you keep telling me to take it up with Harvard/Wiki
See?? There you go again ignoring what I told you about Wikipedia 🙄